Aichinger, Florian On the convergence rate of the fraction of simple algebras. (English) Zbl 1459.08001 Algebra Univers. 81, No. 4, Paper No. 58, 8 p. (2020). If \(P(S,A{\lg _{\rho ,n}})\) is the fraction of simple \(n\)-element algebras of finite type \(\rho \) containing at least one operation symbol of arity \(k \geqslant 3\), then \(P(S,A{\lg _{\rho ,n}}) \geqslant 1 - \exp ( - {n^{k - 1}} + 2{n^{k - 2}} + n\ln (n))\). Reviewer: Jaak Henno (Tallinn) MSC: 08A30 Subalgebras, congruence relations Keywords:simple algebras; probability; fraction of algebras PDF BibTeX XML Cite \textit{F. Aichinger}, Algebra Univers. 81, No. 4, Paper No. 58, 8 p. (2020; Zbl 1459.08001) Full Text: DOI OpenURL References: [1] Bergman, C., Universal Algebra, Fundamentals and Selected Topics. Pure and Applied Mathematics (2012), Boca Raton: CRC Press, Boca Raton · Zbl 1229.08001 [2] Davies, RO, On \(n\)-valued Sheffer functions, Zeitschr. Math. Logik Grundlagen Math., 25, 293-298 (1979) · Zbl 0427.03055 [3] Freese, R., On the two kinds of probability in algebra, Algebra Univ., 27, 70-79 (1990) · Zbl 0692.08007 [4] Murskiĭ, VL, The existence of a finite basis of identities, and other properties of “almost all” finite algebras, Probl. Kibernet., 30, 43-56 (1975) · Zbl 0415.08005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.